## Step-by-step Solution

Problem to solve:

Solving method

Learn how to solve product rule of differentiation problems step by step online.

$\frac{d}{dx}\left(x\right)\sqrt{x^2-1}+x\frac{d}{dx}\left(\sqrt{x^2-1}\right)$

Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule (d/dx)(x(x^2-1)^0.5). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sqrt{x^2-1}. The derivative of the linear function is equal to 1. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two functions is the sum of the derivatives of each function.